Folks, (01)
One reason for introducing a technical term, such as proposition,
is to make distinctions that are confused in more common words
such as 'meaning'. However, technical terms are always defined
in some theory, and people who hold different theories are likely
to have different and incompatible definitions. (02)
Quine has been cited as an authority, and he is for many purposes.
But Q. has stated some strong views, which are not accepted by a
large number of logicians and philosophers. In particular, (03)
1. Q. rejected any version of modal logic. His opposition amounted
to more than merely ignoring it while working on other issues.
Instead, he denied the value, usefulness, or even the possibility
of having a coherent system of modal logic. (04)
2. Point #1 is compatible with Q's denial of any clear or coherent
distinction between intension and extension. That distinction
is central to any version of modal logic, which allows a sentence
s (with no unresolved indexicals) to have different truth values
in different worlds, contexts, or universes of discourse. (05)
3. Since Q's primary work has been in formal logic, he never
developed a complete semantics for natural languages (and he
has been skeptical of the possibility of developing a complete
semantics). Yet he made many comments about various sentences
in NLs and their translations to logic. (06)
4. In those comments, Q. avoided directly addressing the question
of indexicals by coining the term 'eternal sentence' for a sentence
whose referents are all fixed (either bound to explicit quantifiers
or to explicitly named individuals). In effect, he defined that
term to mean 'absence of indexicals' without using the terms
'indexical', 'context', 'possible world', etc. (07)
These views gave Quine's writings an admirable clarity, but at the
expense of ignoring or even deprecating all talk about subjects he
was not prepared to discuss clearly -- which includes the most serious
issues about natural languages. (08)
For these reasons, I believe that taking the word 'proposition' as
synonymous with Q's term 'eternal sentence' would force us to adopt
aspects of Q's philosophy that are incompatible with applications
for which IKL (and other logics) might be used. Among them is the
semantics of NLs, for which many people would like to use IKL. (09)
Since IKL uses the word 'proposition' as a technical term, it is
important to use that word in a way that minimizes confusion among
IKL adopters. I think I agree with Pat about the IKL formalism,
and I think that I know what he meant by the following statements: (010)
1. A proposition has a fixed truth value. (011)
2. But a proposition might have different truth values in different
contexts. (012)
However, this conjunction is likely to cause confusion (or at least
lengthy discussions such as this thread). (013)
My recommendation is to replace the above statements with something
along the following lines: (014)
1. The IKL model theory defines an evaluation function Phi, which
for any proposition p, determines a truth value Phi(p). (015)
2. Inside a nested context, however, the proposition p could have
a truth value that is different from the value Phi(p) that would
be determined outside any nested context. (016)
This avoids the word 'fixed' without introducing the word 'changing'
or any term such as 'proposition-in-a-context'. (017)
John (018)
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